Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.3 The Dot Product - 12.3 Exercises - Page 853: 22

Answer

Angles at vertex $A: \approx 97.7^\circ, B: \approx 53.5^\circ, C: \approx 28.8^\circ$

Work Step by Step

$ \theta = cos^{-1}\dfrac{AB \cdot AC}{|AB||AC|}=cos^{-1}\dfrac{-2}{15}\approx 97.67 ^ \circ$ $ \theta = cos^{-1}\dfrac{AB \cdot BC}{|AB||BC|}=cos^{-1}\dfrac{-11}{3\sqrt {38}}\approx 126.5 ^ \circ$ $ \theta = cos^{-1}\dfrac{AC \cdot BC}{|AC||BC|}=cos^{-1}\dfrac{27}{5\sqrt {38}}\approx 28.8 ^ \circ$ Hence, Angles at vertex $A: \approx 97.7^\circ, B: \approx 53.5^\circ, C: \approx 28.8^\circ$
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